Giorgio del Signore began the goal burst in the 51st minute of the second- round second-leg match, and then Frederic Chassot doubled the home tally four minutes later.
Phil O'Donnell gave Celtic some hope when he replied in the 58th minute, but Shaun Bartlett restored FC Zurich's two-goal advantage three minutes later.
The Scottish champions refused to give up and Henrik Larsson reduced the deficit in the 71st minute. Once again FC Zurich had the answer, though, with Cesar Sant'Anna completing the scoring four minutes later with the sixth goal of the second half.
Cetic's head coach, Jozef Venglos, said: "Because of injuries and suspensions, we had a lot of people playing out of position."
The other Zurich club, Grasshopper, saw their Uefa Cup game against Italy's Fiorentina abandoned after an assistant referee was injured by a firecracker thrown from the crowd.
Philippe Flament was taken to hospital with a knee injury after what was described as "a large firecracker" went off nearby as he walked from the pitch at half-time. Officials abandoned the match without play restarting.
At the time Fiorentina were leading 2-1 on the night and 4-1 on aggregate. It was being played in the southern city of Salerno because of a two-match ban on playing in Florence, following crowd trouble last season.Reuse content